All eyes were low as the first guest arrived
They entered the hall as usually contrived

First came the Doctor muttering orders
Then came a brace of fowl from the waters

A pair of obese ladies entered the scene
Then a blind individual, if you know what I mean.

Some went to the corners and took up their places
Looking around at the expectant faces

There was a knock at the door, though his friend brought the keys
Then a pair of long legs with two dirty knees

The next few to arrive came via Brighton's line
With Mr. Tomas Mix getting here just in time

"Please no more. The house is full!" cried a man in the middle
So no more could enter, as the crowd muttered fiddle.

What has just happened?

Answer

This was a game of bingo

A game where players have pre-printed cards with random numbers from 1 to 90.
A lottery style machine will randomly produce balls with those numbers on which the bingo caller will announce. The players will mark off their numbers when they are called.

Explanation of riddle

All eyes were low = Bingo caller calls "Eyes Down" at the start of a game.
They entered the bingo hall by means of a bingo machine.
Bingo numbers when called are traditionally accompanied with a rhyme or phrase.